Question

question 8
\\(\vec{v}=(9,4)\\)
solve: what is the magnitude of \\(\vec{v}\\)? (answer to 3 decimal places, ex

\\(\vec{u}=(-3,6)\\)
solve: what is the magnitude of \\(\vec{u}\\)? (answer to 3 decimal places, ex

Explanation:

Step1: Recall magnitude formula

For a 2 - dimensional vector $\vec{v}=(x,y)$, the magnitude $|\vec{v}|=\sqrt{x^{2}+y^{2}}$.

Step2: Calculate magnitude of $\vec{v}=(9,4)$

$|\vec{v}|=\sqrt{9^{2}+4^{2}}=\sqrt{81 + 16}=\sqrt{97}\approx9.849$

Step3: Calculate magnitude of $\vec{u}=(-3,6)$

$|\vec{u}|=\sqrt{(-3)^{2}+6^{2}}=\sqrt{9 + 36}=\sqrt{45}\approx6.708$

Answer:

For $\vec{v}=(9,4)$, magnitude is approximately $9.849$.
For $\vec{u}=(-3,6)$, magnitude is approximately $6.708$.